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CHINESE JOURNAL OF PHYSICS
VOL. 46, NO. 1
FEBRUARY 2008
Laser Collimation of a Chromium Beam Using Doppler Force
Wen-Tao Zhang,1, 2 Bao-Hua Zhu,1 Bao-Wu Zhang,3 and Tong-Bao Li3
1
GuiLin University of Electronic Technology, Guilin, China
Department of Physics, Tongji University, Shanghai, China
3
Department of physics, Tongji University, Shanghai, China
(Received August 18, 2006)
2
We report on the collimation of a chromium atomic beam by one-dimensional transverse
Doppler laser cooling. Operated on the cycling 7 S3 → 7 P40 transition at 425.55 nm, the
optical molasses laser power was 60 mW, which was detuned 2.5 MHz below the resonant
frequency. The angular divergence of the atomic beam was reduced from 4.5 mrad to 0.48
mrad, corresponding to a transverse velocity of ±0.46 m/s, and the relevant transverse
temperature is 265 µK.
PACS numbers: 32.80.Pj, 42.50.-P
I. INTRODUCTION
The remarkable capabilities of laser cooling and trapping techniques for the precise
handing of atoms has led to great advances in the field of atom optics. One of the most
promising applications of finely controlled neutral atom beams is direct-write atom lithography of nanometer-scale features, which is called “atom lithography”. This technique
typically uses a series of cylindrical atomic lenses formed by an optical standing wave (SW)
to focus or manipulate atoms and deposit an atomic beam onto a substrate [1]. The collimation of the atomic beams plays an important role in atom lithography technology for
two main reasons: the structure width (SW) deteriorates fast with an increasing divergence
of the atomic beam. Moreover, the SW optical potential is extremely shallow, and so the
atomic velocities along the SW direction must be low for the atoms to be “trapped” in
SW nodes (or antinodes). For these two reasons, a high degree of collimation, typically
less than 1 mrad, of the atomic beam is required. While collimation can be achieved in
a very straightforward way using nozzles and/or collimating apertures, these approaches
generally result in a great loss of flux. Recently, laser cooling techniques, which utilize
dissipative forces to increase the brightness of atomic beams, have arisen as an alternative
that provides high degrees of collimation without a significant loss of flux [2, 3].
Compared with Reference [6], which described the collimation of an atomic gallium
beam by using polarization gradient cooling, this paper describes the collimation of an
atomic chromium beam by using optical molasses. Doppler cooling by optical molasses is
effective for the atoms within the capture velocity region, but polarization gradient cooling is
effective only for the atoms with a very narrow transverse velocity. In this paper, the results
on laser collimation of a thermal 52 Cr beam using one-dimensional transverse Doppler
laser cooling are reported. We have analyzed the optical molasses force on atoms and
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63
c 2008 THE PHYSICAL SOCIETY
OF THE REPUBLIC OF CHINA
LASER COLLIMATION OF A CHROMIUM . . .
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the distribution of atoms for a range of laser detunings. We have also produced a 52 Cr
beam and measured its fluorescence, by which we can determine the angular distribution
of atoms on the beam axis. 52 Cr is particularly interesting because it has some advantages
in atom lithography. First, 52 Cr has the largest abundance (84%) in isotopes, and 52 Cr is
free of hyperfine structure and nucleon spin. Second, 52 Cr has an optical transition from
the ground state to an excited state, it is 7 S3 → 7 P40 , with a wavelength of λ = 425.55 nm
in vacuum, the coherent laser light that is necessary for manipulating 52 Cr can be obtained
from a frequency-doubled Ti:Sapphire laser. Third, the deposited structure of 52 Cr atoms
can be removed directly from the vacuum for direct examination with some microscopy
techniques [4].
II. DOPPLER FORCES ON ATOMS
The spontaneous force is experienced by the neutral atoms in a process of subsequent
directed absorption from a laser beam and isotropic spontaneous emission of photons. Owing to the random direction of the spontaneous emission, there is on average a net momentum transfer in the direction of the absorbed photons. Two low-intensity laser beams of
the same frequency, the same intensity, and the same polarization are directed opposite to
one another (i.e., by retroreflection of a single beam from a mirror), the net force from the
two beams obviously vanishes for atoms at rest. However, atoms moving slowly along the
light beam experience a net force proportional to their velocity whose sign depends on the
laser frequency. If the laser is tuned below the atomic resonance, the frequency of the light
in the beam opposing the atomic motion is Doppler shifted toward the blue in the atomic
rest frame, and is therefore closer to resonance; similarly, the light in the beam moving
parallel to the atom will be shifted toward to the red, further out of resonance. Atoms will
therefore interact more strongly with the laser beam that opposes their velocity and they
will slow down [5, 6].
It is straightforward to estimate the force on atoms from the process of absorption
followed by spontaneous emission. Since the population in the excited state decays at a
rate γ, and in the steady state the excitation rate and the decay rate are equal, so the total
scattering rate γp of light from the laser field is given by
γp =
so γ/2
,
1 + so + (2δ/γ)2
(1)
where so is the saturation parameter which is defined by so = I/Is , Is is the saturation
intensity, for chromium Is = 85W/m2 , and δ is the detuning of the laser frequency from
resonance. From equation (1), the force resulting from absorption followed by spontaneous
emission becomes
~kso /2
Fsp =
.
(2)
1 + so + (2δ/γ)2
It is straightforward to estimate the force on atoms from equation (2). The discussion here
is limited to the case where the light intensity is low enough so that stimulated emission
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FIG. 1: Optical forces vs atomic velocity. The two dotted traces show the force from each beam,
and the solid curve is their sum. The straight line shows how this force mimics a pure damping
force over a restricted velocity range. νc is the capture velocity, these are calculated for so = 1 and
δ = −γ.
is not important. This eliminates any consideration of the excitation of an atom by light
from one beam and stimulated emission by light from the other. In the low intensity case
the forces from the two light beams are simply added to give F~ = F~+ + F~− , where
~
so
~± = ± ~kγ
;
F
2 1 + so + [2(δ ∓ |ωD |)/γ]2
(3)
then the sum of the two forces is
~ ∼
~ =
F
= F~+ + F
8~k2 δso~v
= −β~v ,
γ(1 + so + (2δ/γ)2 )2
(4)
where terms of order (kv/γ)4 and higher have been neglected. Figure 1 shows the optical
force dependence on the velocity, and Figure 2 shows the damping force as a function of
velocity at opposite detuning. From them we can see that for δ < 0 (δ = −γ), this force
~
opposes the velocity and
its
√ therefore viscously damps the atomic motion. F has
√ maxima
0
0 = γ s + 1 is
near v = ±(γ /2k)(X/ 3) and decreases rapidly for larger velocities,
here
γ
o
p
√
the power broadened line-width, X is a numerical factor given by x − 1 + 2 x2 + x + 1,
and x = (2δ/γ 0 )2 . For x >> 1, these maxima appear at v = ±δ/k as expected, so vc = ±δ/k
was defined as the capture velocity [7–11]. From Figure 1, the damping force is efficient
when the velocity of the atoms is smaller than vc , the capture velocity. Figure 3 shows the
force as a function of velocity for an atom in a gradient cooling configuration, which was
used in reference [6]; the inset shows an enlargement of the curve around v = 0. Note the
strong increase in the damping rate over a narrow velocity range that arises from the subDoppler process. In Figure 4 the damping coefficient β for chromium atoms as a function
of the detuning for different values of the saturation parameter so is given. From it we can
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LASER COLLIMATION OF A CHROMIUM . . .
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FIG. 2: The damping force as a function of velocity at opposite detuning.
FIG. 3: The force as a function of velocity for an atom in a gradient cooling configuration with
so = 1 and δ = −γ. The inset shows an enlargement of the curve around ν = 0. Note that the
strong increase in the damping rate over a narrow velocity range that arises from the sub-Doppler
process.
see that for small detuning and low intensity the damping coefficient β is linear in both
parameters. However, for detuning much larger than γ and intensities much larger than
Is , β saturates and even decreases as a result of the dominance of δ. The decrease of β for
large detuning and intensities is caused by saturation of the transition, in which case the
absorption rate becomes only weakly dependent on the velocity. From this simulation, we
can see that the damping coefficient is maximum at s0 = 2 and δ = −0.5γ.
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FIG. 4: The damping coefficient for an atom in a traveling wave as a function of the detuning for
different values of the saturation parameter . The damping coefficient is maximum at s0 = 2 and
δ = −0.5γ.
FIG. 5: Simulative transverse distribution of atoms with cooling laser on and off.
Considering again the example of a chromium atom: we have a 7 S3 → 7 P40 transition
at λ = 425.55 nm, so ~k = 15.6 × 10−28 kgm/s. The spontaneous life of this transition
is 31.77 ns, so the force can be as high as 2.46 × 10−20 N , if 50% of the atoms are in the
excited state, this corresponds to an acceleration of 2.8× 105 m/s2 – much larger than what
is observed with electrostatic or magnetostatic fields.
We consider a simulation of the collimation process that is based on Doppler laser
cooling. The chromium atoms obey a Gaussian distribution at a transversal orientation and
a Maxwell-Boltzmann distribution at longitudinal orientation. Figure 5 shows the simulated
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LASER COLLIMATION OF A CHROMIUM . . .
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FIG. 6: The calculated spatial distributions as a function of the detuning of the cooling laser.
FIG. 7: The transverse velocity of atom vs detuning of cooling laser. For chromium atoms, the limit
temperature is 120 µK and the corresponding transverse velocity is 13.87 cm/s.
distribution of atoms along the transverse direction with and without laser cooling. From
this simulation, we can see that the distribution becomes narrower and the central intensity
becomes stronger with the laser on. Figure 6 shows the simulated spatial distribution of
chromium atoms for different frequency detunings of the cooling laser. For a red-detuned
laser frequency (δ < 0), the atomic beam was collimated and collimation was achieved most
effectively at the detuning of δ = −Γ/2 = −2.5 M Hz for chromium atoms, but for a bluedetuned laser (δ > 0), the atomic beam diverged, this is in good agreement with Figure
2. So in our experiment, we detuned the laser frequency 2.5 MHz below the chromium
atomic resonant frequency. Figure 7 shows the transverse velocity of atoms versus detuning
of the cooling laser. For chromium atoms with the Doppler cooling mechanism, the limit
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FIG. 8: Experimental arrangement. Showing effusive chromium source (at 1650 ◦ C) with 1-mmdiam. aperture, split photodiode for frequency locking, precollimating aperture (3 mm ×1 mm),
collimation region, and fluorescence imaging detector. The optical elements shown are the mirror
(M), beam splitter (PBS), cylindrical lens (CL), and acousto-optic modulator (AOM).
temperature is 120 µK and the corresponding transverse velocity is 13.87 cm/s.
III. EXPERIMENTAL SETUP
Figure 8 shows the experimental arrangement, which includes the vacuum chamber
with atomic beam source, the laser system for atomic beam collimation, and the fluorescence
probe and imaging system used to determine the angular distribution of the atoms on the
beam axis.
The chromium beam was produced using a radiatively heated tungsten crucible with
a 1-mm circular aperture. Typical operating temperatures at 1650 ◦ C produce a most
probable longitudinal velocity of (2kB T /M )1/2 = 960 m/s. The longitudinal velocity distribution was a thermal distribution characterized by the crucible temperature. The beam was
further defined with a 3 mm×1 mm square aperture 450 mm from the crucible. The atomic
beam was then collimated by one-dimensional optical molasses located 20 mm downstream
from the square aperture. For chromium atoms, the 7 S3 → 7 P40 dipole transition was used
for cooling at a wavelength of λ = 425.55 nm (in vacuum), with a line-width of Γ = 5
MHz and saturation intensity I0 = 85 W/m2 . The initial angular distribution entering
the molasses, determined by the 3 mm×1 mm rectangular aperture, had a base width of
approximately 4.5 mrad, for a nominal transverse velocity of ±4.37 m/s. Figure 9 shows
the image of the chromium beam, it indicates that here we have a high quality chromium
atomic beam to be used in experiments.
A frequency-doubled single-mode Ti:Sapphire laser system (MBR–100 and MBD –
200), pumped with 8.5 W by a solid state laser (Verdi –10), typically produced 200 mW–260
mW of blue light at 425.55 nm. The laser was locked to the atomic transition using a split
photodiode technique. An acousto-optic modulator (AOM) was used to detune 2.5 MHz
below the chromium atomic resonant frequency. Another weak beam was chosen as the
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LASER COLLIMATION OF A CHROMIUM . . .
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FIG. 9: The image of the chromium beam.
probe beam, to measure the amount of collimation. In this experiment both the cooling
beam and the probe beam had the same frequency. The cooling laser beam was expanded
using cylindrical lenses to a 1/e2 width of 24 mm along the atom beam and a 1/e2 width
of 3 mm transverse to the atom beam. This laser profile produced our best atomic beam
collimation. Typical powers in the cooling beam ranged from 60 mW to 70 mW, and the
probe beam, also linearly polarized, was circular in cross section with a 1/e2 diameter of
2 mm and had 3 mW power. As Figure 8 shows, the cooling laser beam intersected the
atoms perpendicularly and was retroreflected to form a standing wave. The atoms traveled
660 mm downstream, where they were illuminated transversely by the probe laser. The
probe laser-induced fluorescence from the atoms was collected with a lens and imaged onto
a charged-coupled device (CCD) camera.
The cooling laser was aligned perpendicular to the atomic beam by observing the
fluorescence due to the incident and retroreflected beams with a photomltiplier located
above the cooling region. The cooling laser frequency was scanned over the transition. If the
cooling beam was not perpendicular to the atomic beam, a double peaked fluorescence signal
or a shift in the peak center was observed when the retroreflected beam was on. Iterative
adjustments of the cooling laser direction were made to overlap the two fluorescence peaks.
In this way the cooling laser was aligned perpendicular to the atomic beam to about 1
mrad.
The effect of Doppler laser cooling is presented in Figure 10. CCD images of the
atom beam illuminated by the probe laser are shown. The cooling laser was 60 mW and
detuned −2.5 MHz from resonance. Figure 10 (a) shows the fluorescence of the images of
the uncollimated and collimated atomic beams. A slight asymmetry in the fluorescence line
shape due to the probe detuning is evident, and the measured full width at half maximum
(FWHM) was 7.2 mm and 2.4 mm, respectively. The divergence of the cooled atomic beam
was found to be about 4.5 mrad and 0.48 mrad, the corresponding nominal transverse
velocity was 4.3 m/s and 0.46 m/ s, respectively. Figure 10 (b) shows the profile of the
fluorescence intensity with Doppler cooling off and on. It was in good agreement with the
simulation, as shown in Figure 5.
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FIG. 10: CCD images of laser-induced fluorescence from an atomic chromium beam. (a) the fluorescence of images with laser off and on (b) the profile of fluorescence intensity with Doppler cooling
off and on. Cooling laser 60 mW power, δ = −2.5 MHz.
IV. CONCLUSIONS
We have achieved the collimation of a beam of chromium atoms by Doppler laser
cooling. The atomic beam FWHM was reduced from 7.2 mm to 2.4 mm, and the atomic
beam divergence was reduced from 4.5 mrad to 0.48 mrad.
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